Details

Time bar (total: 7.1s)

analyze627.0ms (8.8%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
6.2%93.6%0.1%6
12.5%87.4%0.1%7
15.6%84.3%0.1%8
18.7%71.8%9.5%9
23.4%56%20.6%10
26.3%52.2%21.5%11
31%40.1%28.9%12
35.6%28.9%35.5%13
36.8%27.5%35.7%14
Compiler

Compiled 18 to 12 computations (33.3% saved)

sample89.0ms (1.3%)

Algorithm
intervals
Symmetry

(sort x y z)

Results
14.0ms256×body128valid
3.0ms66×body128nan
Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify8.0ms (0.1%)

Algorithm
egg-herbie
Rules
25×fma-def_binary64
+-commutative_binary64
*-commutative_binary64
distribute-rgt-out_binary64
associate-+r+_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01218
12316
24316
35916
46116
56216
66216

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
16.2b
Counts
3 → 1
Alt Table
StatusErrorProgram
16.2b
(*.f64 2 (sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))))
Compiler

Compiled 56 to 34 computations (39.3% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.5b
(fma.f64 x (+.f64 y z) (*.f64 y z))
15.3b
(sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))

series199.0ms (2.8%)

Counts
2 → 48
Calls

2 calls:

190.0ms
(sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))
8.0ms
(fma.f64 x (+.f64 y z) (*.f64 y z))

rewrite2.0ms (0%)

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt_binary64
*-un-lft-identity_binary64
sqrt-prod_binary64
add-cube-cbrt_binary64
pow1_binary64
Counts
2 → 25
Calls

2 calls:

1.0ms
(sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))
0.0ms
(fma.f64 x (+.f64 y z) (*.f64 y z))

simplify71.0ms (1%)

Algorithm
egg-herbie
Rules
631×associate-*l*_binary64
605×cancel-sign-sub-inv_binary64
565×associate-*r*_binary64
297×fma-neg_binary64
197×fma-def_binary64
Counts
73 → 70
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02141615
15311523
218731478
349331478
451151478

prune86.0ms (1.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New591170
Fresh000
Picked101
Done000
Total601171
Error
15.7b
Counts
71 → 11
Alt Table
StatusErrorProgram
16.2b
(*.f64 2 (sqrt.f64 (fma.f64 y x (*.f64 z (+.f64 y x)))))
16.7b
(*.f64 2 (sqrt.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))) (cbrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))) (cbrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))))))
61.8b
(*.f64 2 (sqrt.f64 (*.f64 z x)))
16.7b
(*.f64 2 (*.f64 (sqrt.f64 (*.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))) (cbrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))))) (sqrt.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))))))
37.9b
(*.f64 2 (sqrt.f64 (*.f64 y z)))
30.7b
(*.f64 2 (cbrt.f64 (pow.f64 (sqrt.f64 (fma.f64 y x (*.f64 z (+.f64 y x)))) 3)))
47.3b
(*.f64 2 (fma.f64 1/2 (*.f64 z (+.f64 (sqrt.f64 (/.f64 x y)) (sqrt.f64 (/.f64 y x)))) (sqrt.f64 (*.f64 y x))))
63.4b
(*.f64 2 (+.f64 (*.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 z x)))) (+.f64 (*.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 x z)))) (sqrt.f64 (*.f64 z x)))))
16.5b
(*.f64 2 (*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))) (sqrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))))))
17.1b
(*.f64 2 (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))) (cbrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))))) (cbrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))))))
36.3b
(*.f64 2 (sqrt.f64 (*.f64 z (+.f64 y x))))
Compiler

Compiled 2404 to 1163 computations (51.6% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(*.f64 z (+.f64 y x))
1.3b
(fma.f64 y x (*.f64 z (+.f64 y x)))
15.3b
(sqrt.f64 (fma.f64 y x (*.f64 z (+.f64 y x))))

series508.0ms (7.1%)

Counts
3 → 72
Calls

3 calls:

490.0ms
(sqrt.f64 (fma.f64 y x (*.f64 z (+.f64 y x))))
9.0ms
(*.f64 z (+.f64 y x))
8.0ms
(fma.f64 y x (*.f64 z (+.f64 y x)))

rewrite7.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
pow1_binary64
add-cbrt-cube_binary64
Counts
3 → 50
Calls

3 calls:

4.0ms
(*.f64 z (+.f64 y x))
1.0ms
(sqrt.f64 (fma.f64 y x (*.f64 z (+.f64 y x))))
0.0ms
(fma.f64 y x (*.f64 z (+.f64 y x)))

simplify87.0ms (1.2%)

Algorithm
egg-herbie
Rules
608×cancel-sign-sub-inv_binary64
468×times-frac_binary64
347×distribute-rgt-in_binary64
321×distribute-lft-in_binary64
216×fma-def_binary64
Counts
122 → 114
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02492028
16191906
223201861
347051861
454051861

prune177.0ms (2.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1113114
Fresh2810
Picked101
Done000
Total11411125
Error
15.7b
Counts
125 → 11
Alt Table
StatusErrorProgram
63.4b
(*.f64 2 (+.f64 (*.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 z x)))) (+.f64 (*.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 x z)))) (sqrt.f64 (*.f64 z x)))))
37.6b
(*.f64 2 (sqrt.f64 (fma.f64 y x (*.f64 (*.f64 z (sqrt.f64 (+.f64 y x))) (sqrt.f64 (+.f64 y x))))))
16.5b
(*.f64 2 (sqrt.f64 (fma.f64 y x (*.f64 (*.f64 z (*.f64 (cbrt.f64 (+.f64 y x)) (cbrt.f64 (+.f64 y x)))) (cbrt.f64 (+.f64 y x))))))
16.7b
(*.f64 2 (*.f64 (sqrt.f64 (*.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))) (cbrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))))) (sqrt.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))))))
37.9b
(*.f64 2 (sqrt.f64 (*.f64 y z)))
30.7b
(*.f64 2 (cbrt.f64 (pow.f64 (sqrt.f64 (fma.f64 y x (*.f64 z (+.f64 y x)))) 3)))
41.6b
(*.f64 2 (sqrt.f64 (*.f64 x (+.f64 z y))))
36.3b
(*.f64 2 (sqrt.f64 (*.f64 z (+.f64 y x))))
16.7b
(*.f64 2 (sqrt.f64 (*.f64 (*.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))) (cbrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))) (cbrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))))))
47.3b
(*.f64 2 (fma.f64 1/2 (*.f64 z (+.f64 (sqrt.f64 (/.f64 x y)) (sqrt.f64 (/.f64 y x)))) (sqrt.f64 (*.f64 y x))))
16.5b
(*.f64 2 (*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))) (sqrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))))))
Compiler

Compiled 3084 to 1448 computations (53% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(sqrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))))
0.5b
(*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))) (sqrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))))
0.5b
(fma.f64 x (+.f64 y z) (*.f64 y z))
15.3b
(sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))

series308.0ms (4.3%)

Counts
2 → 48
Calls

2 calls:

229.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))) (sqrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))))
79.0ms
(sqrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))))

rewrite23.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
84×sqrt-prod_binary64
64×add-sqr-sqrt_binary64
36×sqrt-pow1_binary64
27×pow1_binary64
18×rem-sqrt-square_binary64
Counts
2 → 106
Calls

2 calls:

8.0ms
(*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))) (sqrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))))
1.0ms
(sqrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))))

simplify107.0ms (1.5%)

Algorithm
egg-herbie
Rules
472×associate-*l*_binary64
445×fma-def_binary64
385×times-frac_binary64
317×associate-/r*_binary64
244×associate-/l*_binary64
Counts
154 → 185
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
05736013
116865614
253605614

prune585.0ms (8.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New4085413
Fresh2810
Picked101
Done000
Total41113424
Error
15.7b
Counts
424 → 13
Alt Table
StatusErrorProgram
63.4b
(*.f64 2 (+.f64 (*.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 z x)))) (+.f64 (*.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 x z)))) (sqrt.f64 (*.f64 z x)))))
16.8b
(*.f64 2 (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))))) (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))))) 3)))
37.6b
(*.f64 2 (sqrt.f64 (fma.f64 y x (*.f64 (*.f64 z (sqrt.f64 (+.f64 y x))) (sqrt.f64 (+.f64 y x))))))
37.9b
(*.f64 2 (sqrt.f64 (*.f64 y z)))
30.7b
(*.f64 2 (cbrt.f64 (pow.f64 (sqrt.f64 (fma.f64 y x (*.f64 z (+.f64 y x)))) 3)))
41.6b
(*.f64 2 (sqrt.f64 (*.f64 x (+.f64 z y))))
16.7b
(*.f64 2 (*.f64 (fabs.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))) (sqrt.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))))))
36.3b
(*.f64 2 (sqrt.f64 (*.f64 z (+.f64 y x))))
47.3b
(*.f64 2 (fma.f64 1/2 (*.f64 z (+.f64 (sqrt.f64 (/.f64 x y)) (sqrt.f64 (/.f64 y x)))) (sqrt.f64 (*.f64 y x))))
16.6b
(*.f64 2 (*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))) (*.f64 (sqrt.f64 (fabs.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))))) (sqrt.f64 (sqrt.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))))))))
16.8b
(*.f64 2 (*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))) (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))))))))
16.5b
(*.f64 2 (sqrt.f64 (fma.f64 y x (*.f64 (*.f64 z (*.f64 (cbrt.f64 (+.f64 y x)) (cbrt.f64 (+.f64 y x)))) (cbrt.f64 (+.f64 y x))))))
41.2b
(*.f64 2 (*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))) (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (+.f64 z x)) (log.f64 y)))))
Compiler

Compiled 20549 to 8694 computations (57.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.5b
(*.f64 (cbrt.f64 (+.f64 y x)) (cbrt.f64 (+.f64 y x)))
0.5b
(cbrt.f64 (+.f64 y x))
1.3b
(fma.f64 y x (*.f64 (*.f64 z (*.f64 (cbrt.f64 (+.f64 y x)) (cbrt.f64 (+.f64 y x)))) (cbrt.f64 (+.f64 y x))))
15.3b
(sqrt.f64 (fma.f64 y x (*.f64 (*.f64 z (*.f64 (cbrt.f64 (+.f64 y x)) (cbrt.f64 (+.f64 y x)))) (cbrt.f64 (+.f64 y x)))))

series292.0ms (4.1%)

Counts
4 → 96
Calls

4 calls:

200.0ms
(sqrt.f64 (fma.f64 y x (*.f64 (*.f64 z (*.f64 (cbrt.f64 (+.f64 y x)) (cbrt.f64 (+.f64 y x)))) (cbrt.f64 (+.f64 y x)))))
48.0ms
(cbrt.f64 (+.f64 y x))
27.0ms
(*.f64 (cbrt.f64 (+.f64 y x)) (cbrt.f64 (+.f64 y x)))
16.0ms
(fma.f64 y x (*.f64 (*.f64 z (*.f64 (cbrt.f64 (+.f64 y x)) (cbrt.f64 (+.f64 y x)))) (cbrt.f64 (+.f64 y x))))

rewrite18.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
30×*-un-lft-identity_binary64
28×cbrt-prod_binary64
23×add-sqr-sqrt_binary64
14×cbrt-div_binary64
14×add-cube-cbrt_binary64
Counts
4 → 96
Calls

4 calls:

8.0ms
(*.f64 (cbrt.f64 (+.f64 y x)) (cbrt.f64 (+.f64 y x)))
2.0ms
(cbrt.f64 (+.f64 y x))
2.0ms
(sqrt.f64 (fma.f64 y x (*.f64 (*.f64 z (*.f64 (cbrt.f64 (+.f64 y x)) (cbrt.f64 (+.f64 y x)))) (cbrt.f64 (+.f64 y x)))))
0.0ms
(fma.f64 y x (*.f64 (*.f64 z (*.f64 (cbrt.f64 (+.f64 y x)) (cbrt.f64 (+.f64 y x)))) (cbrt.f64 (+.f64 y x))))

simplify139.0ms (1.9%)

Algorithm
egg-herbie
Rules
392×times-frac_binary64
320×associate-*r*_binary64
299×fma-def_binary64
244×fma-neg_binary64
237×associate-*l*_binary64
Counts
192 → 224
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
04044499
110204313
234264103
349404103
449604103

prune488.0ms (6.9%)

Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New3355340
Fresh11112
Picked101
Done000
Total33716353
Error
15.5b
Counts
353 → 16
Alt Table
StatusErrorProgram
50.5b
(*.f64 2 (sqrt.f64 (fma.f64 y x (*.f64 (*.f64 z (pow.f64 (pow.f64 x 2) 1/3)) (cbrt.f64 (+.f64 y x))))))
47.3b
(*.f64 2 (fma.f64 1/2 (*.f64 z (+.f64 (sqrt.f64 (/.f64 x y)) (sqrt.f64 (/.f64 y x)))) (sqrt.f64 (*.f64 y x))))
16.5b
(*.f64 2 (sqrt.f64 (fma.f64 y x (*.f64 (*.f64 z (*.f64 (cbrt.f64 (+.f64 y x)) (cbrt.f64 (+.f64 y x)))) (cbrt.f64 (*.f64 (*.f64 (cbrt.f64 (+.f64 y x)) (cbrt.f64 (+.f64 y x))) (cbrt.f64 (+.f64 y x))))))))
63.4b
(*.f64 2 (+.f64 (*.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 z x)))) (+.f64 (*.f64 1/2 (*.f64 y (sqrt.f64 (/.f64 x z)))) (sqrt.f64 (*.f64 z x)))))
16.8b
(*.f64 2 (*.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))))) (pow.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))))) 3)))
37.6b
(*.f64 2 (sqrt.f64 (fma.f64 y x (*.f64 (*.f64 z (sqrt.f64 (+.f64 y x))) (sqrt.f64 (+.f64 y x))))))
37.9b
(*.f64 2 (sqrt.f64 (*.f64 y z)))
62.7b
(*.f64 2 (sqrt.f64 (fma.f64 y x (*.f64 (*.f64 z (*.f64 (cbrt.f64 (+.f64 y x)) (pow.f64 x 1/3))) (cbrt.f64 (+.f64 y x))))))
41.6b
(*.f64 2 (sqrt.f64 (*.f64 x (+.f64 z y))))
16.7b
(*.f64 2 (*.f64 (fabs.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))) (sqrt.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))))))
36.3b
(*.f64 2 (sqrt.f64 (*.f64 z (+.f64 y x))))
63.2b
(*.f64 2 (sqrt.f64 (fma.f64 y x (*.f64 (*.f64 z (*.f64 (cbrt.f64 (+.f64 y x)) (cbrt.f64 (+.f64 y x)))) (fma.f64 1/3 (*.f64 (/.f64 y x) (cbrt.f64 (*.f64 1 (exp.f64 (log.f64 x))))) (cbrt.f64 (*.f64 1 (exp.f64 (log.f64 x)))))))))
16.6b
(*.f64 2 (*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))) (*.f64 (sqrt.f64 (fabs.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))))) (sqrt.f64 (sqrt.f64 (cbrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))))))))
16.8b
(*.f64 2 (*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))) (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))) (sqrt.f64 (cbrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z))))))))
41.2b
(*.f64 2 (*.f64 (sqrt.f64 (sqrt.f64 (fma.f64 x (+.f64 y z) (*.f64 y z)))) (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (+.f64 z x)) (log.f64 y)))))
50.5b
(*.f64 2 (sqrt.f64 (fma.f64 y x (*.f64 (*.f64 z (cbrt.f64 (*.f64 x x))) (cbrt.f64 (+.f64 y x))))))
Compiler

Compiled 12074 to 5298 computations (56.1% saved)

regimes1.7s (23.7%)

Accuracy

Total 0.7b remaining (3.4%)

Threshold costs 0.7b (3.4%)

Counts
226 → 1
Compiler

Compiled 38228 to 19796 computations (48.2% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01016
11316
21316

end13.0ms (0.2%)

Compiler

Compiled 42 to 27 computations (35.7% saved)

sample1.6s (21.9%)

Algorithm
intervals
Results
481.0ms8000×body128valid
132.0ms2300×body128nan
Compiler

Compiled 434 to 247 computations (43.1% saved)

Profiling

Loading profile data...